Introduction to Worst-Case Execution-Time AnalysisPeter Puschner

slides: P. Puschner, R. Kirner, B. HuberVU 2.0 182.101 SS 2016

How do we know the timing is right?

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RTCS

Environment ?

response time

Time in RTS Construction

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DesignArchitecture, resource planning, schedules

Timing AnalysisSchedulability analysis, WCET analysis

Implementation

From Design to Implementation

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T1

T4

T2 T3

t

Task set with precedenceconstraints and deadline

T1 T2 T3 T4t

Task sequence:execution times,response time

Can we guarantee that: response time < deadline?

Timing-Analysis Abstraction

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T1 T2 T3 T4

T1 T2 T3 T4t

In general it is infeasible to model all possible executionscenarios and combinations of task execution times

T1 T2 T3 T4T1 T2T3 T4

Timing analysis abstracts the different execution times of eachtask to one single value ð WCET

TiTi

xt < WCET

xt = WCET

Schedulability and WCET Analysis

Schedulability objects• Units of execution (simple tasks) with WCET• Precedence relations• Synchronization, communication, mutual exclusion• Priorities

WCET-analysis objects• Simple tasks

Interference ... (nasty and therefore widely neglected)• “external” changes of task state that influence exec. time

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• Inputs available at start• Outputs ready at the end• No blocking inside• No synchronization or

communication inside• Execution time variations only

due to differences in• inputs• task state at start time(no external disturbances)

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Task

Input

Output

State

State

Simple Task

Why not just Measure WCET?

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Stop Timing Measurement

Execute Task on Target HW

Start Timing Measurement

WCET estimate ?

Timer,Logic Analyzer,

etc.

Why not just Measure WCET? (2)

• Measuring all different execution traces of a real-size program is intractable in practice.(e.g., mid-size task: 1040 different paths)

• Selected test data for measurement may fail to trigger the longest execution trace.

Rare execution scenarios may be missed (e.g., exception handling, …).

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Static WCET Analysis

Static WCET Analysis: computes upper bounds for the execution time of pieces of code

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Execution time: time it takes to execute• a given piece of code (without disturbance)• in a given application context (inputs, state)• on a given machine

cave: execution time is not response time

Goals for WCET Analysis

WCET analysis = modelingComplexity necessitates modeling tradeoffs

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➭ WCET bounds must be safe➭ WCET bounds should be tight➭ WCET analysis cost should be reasonable

WCET Analysis – Quality

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BCET WCETt

freq

uenc

y

WCET Bound

WCET Determinants

• Possible sequences of actions of the code (= execution paths) in given application[→ code, context]

• The duration of each occurrence of an action on each possible path[→ hardware, state]

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t1

t2t3 t4

t5 t6t7

t8

t8

Task

Exec. Time: Simple vs. Complex Arch.Simple Architecture Model

Duration of each action ai is constant:

xt(pk ) = Σ nk,i t(ai )pk … path k xt(pk ) … WCET of pk

t(ai) … WCET of action ai nk,i … number of times action ai is executed on path pk

Complex Architecture ModelDurations of actions ai vary depending on history:

xt(pk ) = Σ t(ai,j(k) )t(ai,j(k)) … WCET of the jth action ai executed on path k

Reasons: pipelining, caches, parallelism, … 14

WCET Analysis Problems

Path analysis: identifying (in)feasible paths to obtainflow facts• Syntactic restrictions – code• Semantic restrictions – code• Input-data space – application• Automatic analysis vs. user annotations

Modelling of hardware timing• CPU architecture• Implementation of instructions• Resource limitations and state dependencies

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Representation Levels

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Extraction/annotation of possibleexecution paths – flow facts

Execution-time analysis,computation of WCET bound

Translation of flow facts

Source-CodeRepresentation

Machine-LanguageRepresentation

Representation LevelsFlow-fact mapping between representation levels has

to be formally correctà support by the code transformer

otherwise mapping may be ambiguous.

Possible support by code transformer:• emit execution history

(flow facts update by an external tool)

• perform flow facts transformation in parallel to code transformation.

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Generic WCET Analysis Framework

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sourcecode

objectcode

Compilation Transformation ofFlow Facts

Extraction ofFlow Facts

Exec-TimeModeling

WCET

Calculation ofExecutionScenarios

Representation Level

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WCET analysis of Matlab/Simulink models:

Summary

WCET definition• Code; context (application, situation); machine

WCET versus WCET modelling

Problems of the analysis• Flow fact analysis and annotation

• Hardware modeling

• Bridging the representation levels

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